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Question
If a : b = c : d, prove that: xa + yb : xc + yd = b : d.
Solution
Given:
`a/b = c/d`
`(xa+yb)/(xc+yd) = b/d`
The alternendo property of ratios states that if: `a/b = c/d`
`(a+xb)/(c+xd) = b/d`
Rewrite the Left-Hand Side
`(xa+yb)/(xc+yd) = b/d`
Hence, by applying alternendo, we have shown:
`(xa+yb)/(xc+yd) = b/d`
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